A bottom-up packing approach for modeling the constrained two-dimensional guillotine placement problem

Author(s)

Martin, Mateus ^[1] ; Morabito, Reinaldo ^[1] ; Munari, Pedro ^[1]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Prod Engn, Via Washington Luiz Km 235, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Computers & Operations Research; v. 115, MAR 2020.
• Web of Science Citations: 0

Abstract

In this paper, we address the Constrained Two-dimensional Guillotine Placement Problem (C2GPP). This problem considers a rectangular large object and a set of rectangular small item types of given sizes and values. The objective is to select and cut the most valuable subset of small items from the large object using orthogonal guillotine cuts and constrained patterns. To completely model the problem, we present pseudo-polynomial and compact integer non-linear formulations. Then, we obtain an equivalent Mixed Integer Linear Programming (MILP) formulation from each non-linear model. These novel formulations are related to a bottom-up packing approach of successive horizontal and vertical builds of the small items. Additionally, we develop a set of constraints for each model which allows us to strictly consider d-staged guillotine cutting patterns, for a given positive integer d. To evaluate the MILP models and compare their performance to the state-of-the-art formulation of the C2GPP, we run computational experiments using three sets of benchmark instances, two of them from the literature. The results show that the proposed models, based on a bottom-up packing approach, lead to optimal or near-optimal solutions in reasonable processing times, even for scenarios that are intractable for the benchmark model. (C) 2019 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 16/08039-1 - Two-Dimensional Cutting Problems: Mathematical Formulations and Solution Methods
• Grantee: Mateus Pereira Martin
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants